Problem of the Week

Updated at Feb 26, 2024 9:23 AM

This week we have another equation problem:

How would you solve 4(t−3)(2+t)3=563\frac{4(t-3)(2+t)}{3}=\frac{56}{3}?

Let's start!



4(t−3)(2+t)3=563\frac{4(t-3)(2+t)}{3}=\frac{56}{3}

1
Multiply both sides by 33.
4(t−3)(2+t)=564(t-3)(2+t)=56

2
Expand.
8t+4t2−24−12t=568t+4{t}^{2}-24-12t=56

3
Simplify  8t+4t2−24−12t8t+4{t}^{2}-24-12t  to  −4t+4t2−24-4t+4{t}^{2}-24.
−4t+4t2−24=56-4t+4{t}^{2}-24=56

4
Move all terms to one side.
4t−4t2+24+56=04t-4{t}^{2}+24+56=0

5
Simplify  4t−4t2+24+564t-4{t}^{2}+24+56  to  4t−4t2+804t-4{t}^{2}+80.
4t−4t2+80=04t-4{t}^{2}+80=0

6
Factor out the common term 44.
4(t−t2+20)=04(t-{t}^{2}+20)=0

7
Factor out the negative sign.
4×−(t2−t−20)=04\times -({t}^{2}-t-20)=0

8
Divide both sides by 44.
−t2+t+20=0-{t}^{2}+t+20=0

9
Multiply both sides by −1-1.
t2−t−20=0{t}^{2}-t-20=0

10
Factor t2−t−20{t}^{2}-t-20.
(t−5)(t+4)=0(t-5)(t+4)=0

11
Solve for tt.
t=5,−4t=5,-4

Done
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